A closed form solution for stress intensity factors of shear modes for 3-D finite bodies with cracks by energy release rate method

In this paper, a new analytical-engineering method of closed form solution for stress intensity factors of shear modes for 3-D finite bodies with cracks is derived by the time saving energy release rate method. Hence a complete series of useful results of stress intensity factorsK _II andK _III can be obtained. And the results provided by this method are in good agreement with some obtained by other methods.     

圆盘状裂纹前缘塑性区尺寸及张开位移估计

将Ｄｕｇｄａｌｅ模型推广到三维裂纹问题计算了圆盘状裂纹前缘塑性区尺寸,并结合断裂力学中的Ｂａｒｅｎｂｌａｔｔ－Ｄｕｇｄａｌｅ裂纹模型和三维Ｊ－积分原理计算了圆盘状裂纹前缘张开位移,得到了Ｊ－积分与裂纹张开位移的关系,最后用非线性有限元方法对圆盘状裂纹的前缘塑性区尺寸作了数值分析,确定了公式中的未知常数,并对其正确性作了数值验证,本文的工作推广了Ｄｕｇｄａｌｅ模型的应用范围。     

Anti-plane stress intensity, energy release and energy density at crack tips in a functionally graded strip with linearly varying properties

The fracture problem of a crack in a functionally graded strip with its properties varying in a linear form along the strip thickness under an anti-plane load is considered. The embedded anti-plane crack is located in the middle of strip half way through the thickness. The third mode stress intensity factor is derived using two different methods. In the first method, by employing Fourier integral transforms, the governing equation is converted to a singular integral equation, which is subsequently solved numerically by the collocation method based on Chebyshev polynomials. Then, the problem is solved by means of finite element method in which quadrilateral 8-node singular elements around each crack tip are used. After inspecting the validity of the solution technique, effects of crack geometry and non-homogeneous material parameter on the stress intensity, energy release and energy density are studied and the results of analytical and FEM solutions are compared.     

Effect of electric displacement saturation on the stress intensity factor for a crack in a ferroelectric ceramic

A crack in a ferroelectric ceramic with perfect saturation under electric loading is analyzed. The boundary of the electric displacement saturation zone ahead of the crack tip is assumed to be ellipse in shape. The shape and size of ferroelectric domain switching zone near a crack tip is determined based on the nonlinear electric theory. The stress intensity factor induced by ferroelectric domain switching under small-scale conditions is numerically obtained as a function of the electric saturation zone parameter and the ratio of the coercive electric field to the yield electric field. It is found that the stress intensity factor increases as the ratio of the semi-axes of the saturation ellipse increases.